This paper elaborates on the relationship between sustainability of public debt and the debt to GDP ratio in case the interest rate on public debt exceeds the growth rate of GDP. When the primary surplus relative to GDP positively reacts to a higher debt to GDP ratio, a bounded debt to GDP ratio guarantees sustainability. Further, an unbounded debt to GDP ratio is not compatible with sustainability, even if the primary surplus relative to GDP strictly rises as the debt to GDP ratio increases. Finally, sustainability is excluded if the initial debt to GDP ratio exceeds a critical threshold.